422 PROCEEDINGS OF THE AMERICAN ACADEMY §17 



at once reduced to the lorms already obtained by putting 

 We have 



3[:-3;(//«.4§-.)] 



whence, by substitution, we shall find Ee T=^ P,' as before. 

 Disregarding 7^ in comparison with E or P', and treat- 

 ing a; as a constant, we have by ditferentiation, 



_^^ ^ . _ r ^ — 2 -v- r 3 + Gv — 3) er n _ 

 dT 3 ^"^ ^^ U — 3-1 L3-^(^_2)erJ ^ 



"-AT — 3-' ^3 -(- ("^ — 2) ^^ 

 = J1 (6Ar— 15 +er(A^^ — 5.V + 6)) III. 



^7^' 81 l4-7e(v^— 5^^+6) (6;i'— i5+7e(.v^— 5;^-t-6)) j * 



etc. 



From equations III. it is easil}^ seen that x cannot be 

 constant and less than 3, since it is well known that the 

 rate of expansion increases with the temperature. 



There is much however to indicate for x a smaller value 

 than 6; the rate of expansion does not increase quite so rap- 

 idly on the whole as our first analysis would indicate, and 

 from the analogy of small magnets we should expect that at 

 short distances the attraction should vary, for compound 

 substances, inversely as some power of the distance be- 



* It will be noticed that the value of x is here greater by 2 units than in { 2, denoting the 

 rate of variation of the pressure, not the attraction. 



